- #1
imlala
- 3
- 0
Homework Statement
Hello,
I'd like to prove that the category cmon of commutative monoids has binary products.
The Attempt at a Solution
actually I'm aware that i have to use cartesian products
given monoids (M, [tex]\bullet[/tex]m, [tex]e^{}_{m}[/tex]) and (N, [tex]\bullet[/tex]n, [tex]e^{}_{n}[/tex])
it follows that (M[tex]\times[/tex]N) [tex]\times[/tex] (M[tex]\times[/tex]N) [tex]\rightarrow[/tex] M[tex]\times[/tex] N
and ((m,n), (m',n')) |---> (m [tex]\bullet[/tex]m m', n [tex]\bullet[/tex]n n') ...
Thanks in advance for any help!